The Arbitrage Pricing Theory and Supershares - Latham, Mark (Journal of Finance, 1989)
In a single-period model with options on the market portfolio, linear factor pricing holds if and only if the variance of the market conditional on the factors is zero. There is no need for factors other than nonlinear functions of the market. For accurate linear pricing of all payoff patterns the factors must be rotationally equivalent to Hakansson's “supershares.” In a multiperiod model, a similar set of results holds, but with consumption replacing the market payoff. The methodology of the empirical Arbitrage Pricing Theory literature is not consistent with either the single-period model or the multiperiod model.